Question: Simplify the following expression: $\dfrac{72y^5}{24y^4}$ You can assume $y \neq 0$.
Solution: $ \dfrac{72y^5}{24y^4} = \dfrac{72}{24} \cdot \dfrac{y^5}{y^4} $ To simplify $\frac{72}{24}$ , find the greatest common factor (GCD) of $72$ and $24$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $24 = 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(72, 24) = 2 \cdot 2 \cdot 2 \cdot 3 = 24 $ $ \dfrac{72}{24} \cdot \dfrac{y^5}{y^4} = \dfrac{24 \cdot 3}{24 \cdot 1} \cdot \dfrac{y^5}{y^4} $ $\phantom{ \dfrac{72}{24} \cdot \dfrac{5}{4}} = 3 \cdot \dfrac{y^5}{y^4} $ $ \dfrac{y^5}{y^4} = \dfrac{y \cdot y \cdot y \cdot y \cdot y}{y \cdot y \cdot y \cdot y} = y $ $ 3 \cdot y = 3y $